power builder you are correct to a point but i think fadi was just refering to the targeted muscles, all exercises require stabilizing muscles... this is just about the targeted muscles.I am positive your abs will never give out while doing bicep curls!
I belieive however that lying incline db bicep curls are the best, as they stretch the two major muscles to a maximum range, while you are doing teh exercise, over the maximum range of motion. Because you are lying the core strength is mostly negated as your body is fully supported by the bench.
Also even if standing your core remians tight, but it is not, "getting a workout" maybe if you are doing bw military presses it is getting a blast.